According to the sources, Rohani is also willing to allow international inspectors to monitor the dismantling of the Fordo reactor.
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Washington has imposed sanctions restricting US entities' trade with and provision of services to Iran in a dispute over Tehran's nuclear program. The June election of centrist cleric Hassan Rouhani to the presidency has raised hopes of a settlement and lifting of some sanctions.
Iranian officials and opposition figures alike have criticized the sanctions for blocking vital imports, while dissidents say they hurt their ability to organize.
The June election of President Rohani has raised expectations of a negotiated settlement to Iran's nuclear dispute with the West and a lifting of some sanctions. The West accuses Iran of seeking to develop nuclear weapons, but Tehran says its research has purely peaceful, civilian aims.
Tehran maintains an extensive web filter and blocks sites it deems critical of the government, including Karoubi's personal site, which includes statements, pictures, a biography and news related to the former parliament speaker.
The US Treasury Department loosened some sanctions in May, issuing a general license allowing US firms to sell services and technology used for personal communications to Iranians.
Iranian nuclear chief Ali Akbar Salehi said Monday that both Iran and world powers had to approach nuclear talks in good faith so as to create a "win-win" result.
But he said the chances of progress were improved by the unity among Iran's new political leadership over what it sought in the next round of talks and what it was prepared to give the world powers.
Salehi spoke outside of a 159-nation conference of the UN's International Atomic Energy Agency that is expected to touch on fears over Tehran's nuclear aims.
Iranian President Hasan Rohani is expected to affirm his commitment to trying to ease tensions in comments to the UN General Assembly this week.
Even with the recent installment of Rohani and his relatively moderate aides, Ayatollah Ali Khamenei remains the top decision maker on the nuclear and other issues as the country's supreme leader.
In Tehran on Monday, state TV quoted Foreign Ministry spokeswoman Marzieh Afkham as warning that "threatening language against Iran" will backfire, adding: "Interaction with Iran will be possible only through respect."
Reuters, AP contributed to this report
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